Mel-- An Army or AAF Unit with a four digit designation usually designates a sub-unit of some larger component--usually in the support role.Such as Quartermaster, Air Base Unit, Motor Pool, Depot Repair etc.
The earliest reference I could find to the 4511th was a Combat Crew Training Squadron in the early 50s.This may well have been its mission in WW2 as well.When I first saw the number in your post I thought it might be an Air Base Unit.
Do you have any photos of your grandfather in uniform?The insignia might give us a clue as to where he served.
Where did you get the number 4511th from? If from his discharge papers there is a great deal more information that can be had from it.
Barksdale, LA, became the home base of the 8th Air Force after the war.It is a possibility that his 4511th was affiliated with the USAAF and possibly the 8th AAF.